Exercise 4 Page 589

We will list two ways to determine whether a chord is a diameter. To do so, we will consider the results of Exploration I and Exploration II. Let's start!

Result of Exploration I

In order to construct a circle we need the radius and the center of the circle.

Remember that the diameter is twice the radius. Therefore, if the length of chord is twice the radius, then we can conclude that the chord is a diameter.

Result of Exploration II

In Exploration II, we saw that if a chord of a circle is the perpendicular bisector of another chord, then it contains the center of the circle.

Therefore, since a diameter is a chord that passes through the center, we can conclude that the chord that is the perpendicular bisector is a diameter.